What happens to the total resistance in a wire if the length is doubled?

• A. Resistance is unchanged
• B. Resistance is doubled
• C. Resistance is halved
• D. Resistance is tripled

Answer: (B)

The correct answer is that resistance is doubled. This principle is rooted in the fundamental relationship between resistance, length, and cross-sectional area as described by Ohm's Law and the resistivity equation.

Resistance in a conductor is directly proportional to its length. This means that if you double the length of the wire, you are effectively increasing the distance that electrons must travel through the material. As electrons encounter more of the atomic structure within the wire over this longer distance, they experience more collisions, which leads to increased resistance.

The formula for resistance (R) is given by ( R = \rho \frac{L}{A} ), where ( \rho ) is the resistivity of the material, ( L ) is the length of the wire, and ( A ) is the cross-sectional area. In this formula, you can see that resistance increases linearly with length. Therefore, if the length is doubled (while keeping the area and material constant), the resistance also doubles.

This understanding is critical for applications in electrical engineering and electrical systems, where controlling resistance can impact the efficiency and functionality of circuits and devices.